Rewrite as a simplified fraction. ${3.91\overline{5} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3915.5555...\\ 100x &= 391.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3524}$ ${x = \dfrac{3524}{900}} $ ${x = \dfrac{881}{225}} \text{or} {3 \dfrac{206}{225}}$